1. Let [math]f\left(x\right)=x^2-5x+2[/math]. (This is the same quadratic we used in Chapter 1.) Find a constant Taylor polynomial for [math]f\left(x\right)[/math] centered at [math]x=1[/math].
2. Now, find a linear Taylor polynomial for [math]f\left(x\right)[/math] centered at [math]x=1[/math].
3. Graph [math]f\left(x\right)[/math] and both constant and linear Taylor polynomials on the set of axes below.
4. What do you notice? What can you say about these Taylor polynomials near the point [math]\left(1,f\left(1\right)\right)[/math] ?